I'm assuming each turn is independent of all other turns, so I don't care if anyone else is playing or not.

Thanks.  That's the 6th 0.1 BTC you've sent me.  I've lost the first 5 back to you, and will probably do the same now with this one.

There's a problem:



The 3rd address was 15cVZLDWCmmHZjHXSFnj5sWUKVbtUmip2Y, not what is shown on the site.

Oh, now it's right after I refreshed the page:



Are you updating the page by hand?

I realised that.  But I also had found an argument that convinced me that I had a negative expectation, which contradicted what I already knew.  So I wanted to clear things up and understand what was wrong with my argument.

Turns out my argument was just saying that the most likely result was that I would lose, which is true, and doesn't contradict that the EV is 0.

If you want to use the word 'bitcoin' because it's search engine friendly, do so - just multiply the amount won by the price-per-chip in bitcoins.  So when he wins 23 chips, write:

  User: avl42 won 0.002 Bitcoin playing Roulette

Then it's true as well as searchable!  

Edit: otherwise people use "bitcent" for 0.01 BTC or "1 mBTC" for 0.001 BTC.  Neither one is good for SEO purposes though I'm guessing.

(07:39:32 PM) deb: You people really get off on this shit don't You?
(07:39:57 PM) Chris: it's not a sexual thing
(07:40:04 PM) deb: i mean no disrespect, i just can't fathom where making charts to work out gambling strategies that don't really matter is a good thing to do
(07:40:04 PM) Chris: it's more of an obsessive thing
(07:40:12 PM) Chris: I couldn't relax before I understood wtf was going on

Yes.  Once I've started playing the 1 game (A?), I only play the 2 game (B?) if I've won more than I've lost at A.  So when my wins and losses eventually match, A will have more wins than losses, and B will have more losses than wins, and so I'll be making a loss overall.

It's OK that the most common result (which is #wins == #losses) is a net loss, because the whole curve is skewed to the left.  The most likely final balance is a little less than the starting 1000, but there's a good sized chunk of significant winnings to the right.  Overall, the average is 1000:



Edit: Notice how the likely range of balances when I lose (600-1000) is half as wide as the likely range of balances when I win (1000-1800).

The red (losing) area is twice the size of the green (winning) area, so we're twice as likely to lose as to win.  But it's much narrower, so if we lose, we don't lose much, but if we win, we're likely to win a decent amount.

I regularly see the ball staying in one spot as the wheel spins, and assumed that was happening while the client communicated with the server to see where the ball should land.  But one time the wheel froze as well, which is different.  And the ball landed in a different slot than the text said it did (as shown in the screenshot I posted).

I'd like an option to speed up (or remove) the animation.  I don't want or need the spinning wheel graphics, and waiting for it is kind of frustrating after a while.

Yes, I realise.  That's what I was getting at with:


But I was wondering how it was possible that the expected return wasn't at least slightly lower than zero, given that crossing from 1000 to 998 effectively "wastes" a loss.

I think I have a reasonable explanation of that now:

The losses incurred each time we cross from 1000 to 998 are offset by the fact that winnings are slightly skewed upwards.  For example, if we win our first 5 bets, we win 10 coins, but if we lose our first five bets, we lose only 6 coins.  So the expected return can be thought of in a hand-waving way as:

  (p(lots more wins than losses) * big_win) +
  (p(lots more losses than wins) * smaller_loss) +
  (p(similar wins and losses) * loss_due_to_crossings_from_1000_to_998)

where the first term is cancelled out by the other two.

It's very rough and ready, but I think that's enough to let me stop thinking about it!

I started with 1000 chips, and tossed the coin 1 billion times.

I got 499985225 wins and 500014775 losses
29550 more losses than wins
and a final balance of -36034

Each of the 29550 excess losses should have lost me 1 chip, so I should be at -28550, but I'm 7484 chips short of that.

I got the simulation to print out each time the number of wins and losses were the same.  The last time that happened before the billionth turn was after 612,215,220 turns, at which point there had been 306107610 wins and 306107610 losses, and the balance was -6484.  ie. 7484 below where I started.  This suggests to me that the balance crossed from 1000 to 998 7484 times, 'wasting' 1 win each time.

I suspect that the 7484 crossings is insignificant compared to the amounts won and lost, and that's why the expected return is still 0.  Could that be the case?

Edit: I left the simulation running.  After 2 billion tosses I was back in profit:

2000000000 turns; 1000008100 wins; 999991900 losses; 16200 more wins than losses; 6002 balance

the last time the numbers of wins and losses were the same:

1821704084 turns; 910852042 wins and 910852042 losses; -8477 balance

so now there have been 9477 crossings from 1000 to 998, and my balance is only positive because I have been lucky; even though I've have had 16k more wins than losses, I'm only 5k up.

Here's the Python script I used by the way: http://pastie.org/5439806

Yes, it sounds stupid, but probably is just as valid as my argument.  With your scheme it takes 2 losses to fall to 999 from 1001, but only one win to recover.  So it is a winning strategy.

Now that's got to be wrong...  Just wish I could see why!

I'm thinking that since it's a fair coin, my path will be essentially a random walk through profit and loss.  So if I do win the first trial, at some point in the future I'll be back to 1000 coins, and can effectively discount all the coin tosses in between, since the wins and the losses will be equal.

If I lose that first trial, or any trial when my balance is 1000, I'll lose 2 coins and 'waste' 2 wins getting back to even.  Other than that everything seems equal, so it appears to me that this case, which will keep happening each time I cross from 1000 to 998, will result in me losing in the long run.

I agree that this is probably incorrect, but can't see the hole in my reasoning.


I will do.  Here's a worked example of how I get 22 wins and only 20 losses, but break even:

I've always thought that it's not possible to change the expected return of a game with fixed odds by altering your bet size.  I've seen this stated all over the place.

For the last hour or two I've been playing roulette at luckybitcoincasino, and seem to have found a way of reducing my expected return.

I was betting the 3-36 line over and over, starting with 100 chips.  I was betting 2 chips each spin, but whenever I fell below 70 chips I was reducing my bet to 1 chip per spin, and increasing it back to 2 chips per spin when I got back to 70 chips.

I counted my wins and losses.  Each time my number of wins was exactly equal to half my number of losses, I noticed my balance was a little lower than the previous time it happened.

I would expect that since a win pays out twice as much as a loss loses, having N wins and 2N wins losses should mean I was breaking even, but that wasn't the case.

I tried to understand why, and came up with this thought experiment:


So what's wrong with the above argument?  It looks to me like I've found a strategy that reduces my expected return, making it negative in a zero-expectation coin toss game.  I must be missing something.  Mustn't I?

I ended up getting bored, increasing my bet size, and losing it all.

I kept track of the results.

Betting on the 3-36 line, I had 191 losing spins, 84 winning spins, and 8 zeroes, which also counted as wins.

So even with the extra wins from the zeros, I still had more than twice as many losses as wins.

Stats:


I guess once again I was just unlucky...  It's a good thing I don't gamble, eh? 

There doesn't seem to be a difference between play and real money as far as the 3-36 line paying out on zero too.

I did a few hundred spins, and even though the odds are in my favour, I'm still losing.

I just had a weird spin.  The animation kind of stuttered, and the ball landed somewhere other than where the game said it did.

Here's a screenshot (in which you can also see how well I'm doing 'exploiting' your bug...):

Thanks.

Would it be rude to play the 3-36 line on roulette with the free chips?  

Edit: I logged in, and the site tells me: "You have 0 chips."

Edit2: Because you sent them to my wallet, not my casino account.  So now I have to wait for 3 confirmations - which is probably long enough for your programmer to fix the bug. 

I'm not convinced.  I think it's possible that your scheme could result in a less stable difficulty, with the difficulty adjustment continuously overshooting, overcorrecting.  Like watching a novice trying to steer a boat.

Fixed that for you. 

I think the point is that you could easily add in a bunch of imaginary winning games to make it look like on average the site is performing as advertised.  Nobody could prove that the added games weren't real.

It's still interesting to see the list of recent games.  I just don't think it really proves anything.  (Not like your provably fair hashes do).

I can duplicate it just fine.

If the game wasn't quite so slow I would duplicate it over and over and win some bitcoins, but I don't have the patience.

Here's a screenshot of it happening though since the site owner doesn't seem to want to believe you: